Xét \(x\le2010\Rightarrow2010-x+2011-x=2012\Rightarrow x=\frac{2009}{2}\left(TM\right)\)
Xét \(2010< x< 2011\Rightarrow x-2010+2011-x\Rightarrow1=2012\left(loại\right)\)
Xét \(x\ge2011\Rightarrow x-2010+x-2011=2012\Rightarrow x==\frac{6033}{2}\left(TM\right)\)
Vậy \(x\in\left\{\frac{2009}{2};\frac{6033}{2}\right\}\)